On the closure-preserving sum theorem
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- by M. K. Singal and Shashi Prabha Arya PDF
- Proc. Amer. Math. Soc. 53 (1975), 518-522 Request permission
Abstract:
The closure-preserving sum theorem holds for a property $\mathcal {P}$ if the following is satisfied: “if $\{ {F_\alpha }:\alpha \epsilon \Omega \}$ is a hereditarily closure-preserving closed covering of $X$ such that each ${F_\alpha }$ possesses the property $\mathcal {P}$, then $X$ possesses $\mathcal {P}$". A general technique for proving this theorem is developed. The theorem is shown to hold for a large number of topological properties. As an application, three general sum theorems have also been obtained.References
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Additional Information
- © Copyright 1975 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 53 (1975), 518-522
- MSC: Primary 54B99
- DOI: https://doi.org/10.1090/S0002-9939-1975-0383335-6
- MathSciNet review: 0383335